Points of order $13$ on elliptic curves

Kamienny, S.; Newman, Burton

doi:10.7169/facm/1666

Search citation statements

Order By: Relevance

Paper Sections

Select...

Elliptic Curves With C 13 Torsion Over Quadratic Fields1

Citation Types

Supporting

Mentioning

Contrasting

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 15 publications

(27 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 2.2. See [6] for a different proof, using the fact that X 1 (13) is bielliptic, of the fact that rank of J(Q(ζ 13 ) + ) is 0.…”

Section: Elliptic Curves With C 13 Torsion Over Quadratic Fieldsmentioning

confidence: 99%

Tamagawa Numbers of elliptic curves with 𝐶₁₃ torsion over quadratic fields

Najman

2017

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Let E be an elliptic curve over a number field K, cv the Tamagawa number of E at v, and let cE = v cv. Lorenzini proved that v13(cE) is positive for all elliptic curves over quadratic fields with a point of order 13. Krumm conjectured, based on extensive computation, that the 13adic valuation of cE is even for all such elliptic curves. In this note we prove this conjecture and furthermore prove that there is a unique such curve satisfying v13(cE) = 2.

show abstract

“…Remark 2.2. See [6] for a different proof, using the fact that X 1 (13) is bielliptic, of the fact that rank of J(Q(ζ 13 ) + ) is 0.…”

Section: Elliptic Curves With C 13 Torsion Over Quadratic Fieldsmentioning

confidence: 99%